In section  we will emphasize that both of the latter amendments
are essential. They will be shown to lead to
a decisive ultimate simplification of
correspondence between spaces \({\cal L}\)  and \({\cal H}_{phys}\) .
In the same section we will also
recall our recent letter [1]}
where we described the first nontrivial implementation
of the idea.
Basically, we just considered \(N=2\)  and
proposed there a modified and slightly amended
version of the Bender-inspired \({\cal PT}-\) symmetric
quantum mechanics. Although we encountered there
certain conceptual obstacles (so that we simply
did not think about \(N>2\) ),
still, letter [1]} can be perceived
as a basic inspiration of our present
message.
